Backups on user end

I'm told our Zimbra mail server will only keep 3 days worth of data, and that the people who administrate that server say it's not their policy to take care of backups for users.
I'm trying to figure out a way to backup for our users without having to touch the server at all, and without having any data stored on the local machines for security reasons.
Preferably, the determined method will work through the Zimbra Web Client since that's what my users are already using and so that we won't have to maintain a desktop client program. However, I could not figure out a way to do that, so I have a Rube Goldberg-machine type setup, something that seems overly complicated for what I"m trying to do. On a couple of test computers, I've installed the Zimbra desktop client and configured zdrun.vb to place any local data (like the .msg files, whatever can be done with those) onto a network drive.

Then, the desktop client is configured to run a backup every day. Since we don't want to switch to the desktop client, this process can be intrusive because the user will have to close out of the client after it's done backing up. Another concern is that the client may not back up as soon as it starts up. If someone comes in late one day at around noon, the client will make backups at noon for the rest of the week until it misses a couple of days over the weekend and returns to the normal schedule. Editing the zdrun file also seems unstable, since sometimes the client doesn't seem to start at all.

TL;DR: Are there any options for users to backup mail through web client? If not, what are best practices for backing up using the desktop client (or any other method that does not involve the ZCS server)?